%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:33:04 AM UTC 2026
% Result : Theorem 14.59s 2.56s
% Output : CNFRefutation 14.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 10 unt; 0 def)
% Number of atoms : 135 ( 43 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 67 ~; 62 |; 4 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 70 ( 1 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X1,X0))
=> ( subset('identity$urelation$uof'(X1),X2)
=> ( subset(X1,range(X1,X0,X2))
& X1 = domain(X1,X0,X2) ) ) ) ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ( subset('identity$urelation$uof'(X1),X2)
=> ( X1 = range(X0,X1,X2)
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ) ).
fof(p5,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
<=> 'ilf$utype'(X1,'relation$utype'(X0,X0)) ) ) ) ).
fof(p30,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> domain(X0,X1,X2) = 'domain$uof'(X2) ) ) ) ).
fof(p32,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> range(X0,X1,X2) = 'range$uof'(X2) ) ) ) ).
fof(p34,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_44,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
=> ( subset('identity$urelation$uof'(X0),X1)
=> ( X0 = range(X0,X0,X1)
& X0 = domain(X0,X0,X1) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
=> ( subset('identity$urelation$uof'(X0),X1)
=> ( X0 = range(X0,X0,X1)
& X0 = domain(X0,X0,X1) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_44]) ).
cnf(c0,plain,
( X1 = domain(X1,X2,X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ subset('identity$urelation$uof'(X1),X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c3,plain,
( ~ subset('identity$urelation$uof'(X2),X0)
| ~ 'ilf$utype'(X1,'set$utype')
| X2 = range(X1,X2,X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c8,plain,
( 'ilf$utype'(X1,'relation$utype'(X0,X0))
| ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p5]) ).
cnf(c63,plain,
( domain(X0,X1,X2) = 'domain$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p30]) ).
cnf(c65,plain,
( range(X0,X1,X2) = 'range$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p32]) ).
cnf(c67,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p34]) ).
cnf(c69,plain,
'ilf$utype'(sK86,'identity$urelation$uof$utype'(sK85)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c70,plain,
subset('identity$urelation$uof'(sK85),sK86),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c71,plain,
( sK85 != range(sK85,sK85,sK86)
| sK85 != domain(sK85,sK85,sK86) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'ilf$utype'(X0,'identity$urelation$uof$utype'(X1))
| 'ilf$utype'(X0,'relation$utype'(X1,X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c67,c8]) ).
cnf(d1,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| range(X0,X1,X2) = 'range$uof'(X2) ),
inference(resolution,[status(thm)],[c67,c65]) ).
cnf(d2,plain,
( ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| range(X0,X0,X1) = 'range$uof'(X1) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| range(X0,X0,X1) = 'range$uof'(X1) ),
inference(resolution,[status(thm)],[c67,d2]) ).
cnf(d4,plain,
( ~ 'ilf$utype'(sK85,'set$utype')
| range(sK85,sK85,sK86) = 'range$uof'(sK86) ),
inference(resolution,[status(thm)],[d3,c69]) ).
cnf(d5,plain,
range(sK85,sK85,sK86) = 'range$uof'(sK86),
inference(resolution,[status(thm)],[c67,d4]) ).
cnf(d6,plain,
( ~ subset('identity$urelation$uof'(X0),X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X1,X0))
| ~ 'ilf$utype'(X1,'set$utype')
| X0 = range(X1,X0,X2) ),
inference(resolution,[status(thm)],[c67,c3]) ).
cnf(d7,plain,
( ~ subset('identity$urelation$uof'(X0),X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X1,X0))
| X0 = range(X1,X0,X2) ),
inference(resolution,[status(thm)],[c67,d6]) ).
cnf(d8,plain,
( ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ subset('identity$urelation$uof'(X0),X1)
| X0 = range(X0,X0,X1) ),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( ~ subset('identity$urelation$uof'(X0),X1)
| ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| X0 = range(X0,X0,X1) ),
inference(resolution,[status(thm)],[c67,d8]) ).
cnf(d10,plain,
( ~ 'ilf$utype'(sK86,'identity$urelation$uof$utype'(sK85))
| sK85 = range(sK85,sK85,sK86) ),
inference(resolution,[status(thm)],[d9,c70]) ).
cnf(d11,plain,
( ~ 'ilf$utype'(sK86,'identity$urelation$uof$utype'(sK85))
| sK85 = 'range$uof'(sK86) ),
inference(demodulation,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
sK85 = 'range$uof'(sK86),
inference(resolution,[status(thm)],[c69,d11]) ).
cnf(d13,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| domain(X0,X1,X2) = 'domain$uof'(X2) ),
inference(resolution,[status(thm)],[c67,c63]) ).
cnf(d14,plain,
( ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| domain(X0,X0,X1) = 'domain$uof'(X1) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| domain(X0,X0,X1) = 'domain$uof'(X1) ),
inference(resolution,[status(thm)],[c67,d14]) ).
cnf(d16,plain,
( ~ 'ilf$utype'(sK85,'set$utype')
| domain(sK85,sK85,sK86) = 'domain$uof'(sK86) ),
inference(resolution,[status(thm)],[d15,c69]) ).
cnf(d17,plain,
domain(sK85,sK85,sK86) = 'domain$uof'(sK86),
inference(resolution,[status(thm)],[c67,d16]) ).
cnf(d18,plain,
( sK85 != range(sK85,sK85,sK86)
| sK85 != 'domain$uof'(sK86) ),
inference(demodulation,[status(thm)],[c71,d17]) ).
cnf(d19,plain,
( sK85 != 'domain$uof'(sK86)
| sK85 != 'range$uof'(sK86) ),
inference(demodulation,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
( ~ subset('identity$urelation$uof'(X0),X2)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| X0 = domain(X0,X1,X2) ),
inference(resolution,[status(thm)],[c67,c0]) ).
cnf(d21,plain,
( ~ subset('identity$urelation$uof'(X0),X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| X0 = domain(X0,X1,X2) ),
inference(resolution,[status(thm)],[c67,d20]) ).
cnf(d22,plain,
( ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ subset('identity$urelation$uof'(X0),X1)
| X0 = domain(X0,X0,X1) ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( ~ subset('identity$urelation$uof'(X0),X1)
| ~ 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| X0 = domain(X0,X0,X1) ),
inference(resolution,[status(thm)],[c67,d22]) ).
cnf(d24,plain,
( ~ 'ilf$utype'(sK86,'identity$urelation$uof$utype'(sK85))
| sK85 = domain(sK85,sK85,sK86) ),
inference(resolution,[status(thm)],[d23,c70]) ).
cnf(d25,plain,
( ~ 'ilf$utype'(sK86,'identity$urelation$uof$utype'(sK85))
| sK85 = 'domain$uof'(sK86) ),
inference(demodulation,[status(thm)],[d24,d17]) ).
cnf(d26,plain,
sK85 = 'domain$uof'(sK86),
inference(resolution,[status(thm)],[c69,d25]) ).
cnf(d27,plain,
sK85 != 'range$uof'(sK86),
inference(resolution,[status(thm)],[d26,d19]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[d27,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 08:04:51 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.59/2.56 % SZS status Theorem for theBenchmark.p
% 14.59/2.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------